In German Pat. No. 1,258,189 and German DT-OS No. 2,249,838, ignition systems for internal combustion engines with a plurality of cylinders are disclosed. However, in these systems, the spark generating signals which are shifted by predetermined angles relative to each other are generated by a plurality of individual electronic ignition systems, one for each ignition coil. The shifting of the spark generating signal is controlled by the position signal furnishing means, that is by a sensing system which senses markings or other indicators placed at predetermined angular intervals around the circumference of a rotating shaft in the engine. The ignition systems are energized in a predetermined order in accordance with the so-furnished position signals. This requires a very great amount of equipment in particular for complicated ignition systems which include computing stages for determining the time for which a switch controlling the current through an ignition coil is closed, as well as the angle at which the switch is to be opened. In another system, disclosed in U.S. Pat. No. 3,943,898, a reference marking on the position signal generating means is electronically multiplied and the so-multiplied signal applied to an ignition computer. The position signal furnishing means are therefore particularly simple but the ignition computer is relatively expensive.